The cubs were born within five hours of each other on Saturday, triggering "pandamonium" at the much-visited zoo in the US capital.
"Our panda cubs are doing well, but the panda team had a challenging night," the zoo said in a brief statement.
Mei Xiang has been caring for the delicate and vulnerable newborns one at a time -- but when handlers tried late Sunday night to swap the cubs, she refused to let go of the one in her possession.
Prior to the swap, the smaller cub was fed formula first by bottle, then by tube, with the latter procedure turning out to work "well and quickly."
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"Our goal is for each cub to spend an equal amount of time with their mother. The newborn cubs are vulnerable and this first week is incredibly important and the risk remains high," the National Zoo said.
The first tiny cub -- pink, hairless and only about the size of an adult mouse -- was born at 5:35 p.M. (2135 GMT) Saturday and Mei Xiang reacted by tenderly picking it up.
While panda twins are not uncommon in the wild, they need intensive maternal care after birth, making survival precarious.
Mei Xiang's cubs are the third set of twins born in captivity in the United States. Only one set, born in 2013 at the Atlanta zoo, has survived.
Experts feel the best way to keep both cubs alive is to keep swapping them, so they each get quality time with their mother.
Still to be determined are the cubs' sex -- and father.
But she was also inseminated with fresh semen from the National Zoo's resident male giant panda Tian Tian. DNA tests will establish which is the father.